Brush each flatbread lightly with olive oil, then top each with a quarter of the sliced peaches and a quarter of the cheese. Season with salt and pepper. Place flatbreads on baking sheets and bake for ten minutes, until the crust is golden and the cheese is melted.

Meanwhile, combine balsamic vinegar and sugar in a small sauce pan, bring to a boil, then simmer on low until the mixture has reduced by half (approximately five minutes). Transfer to a small pitcher or bowl.

In a separate bowl, toss arugula with a splash of balsamic vinegar and splash of olive oil. Season with salt and pepper.

Remove flatbreads from oven, then top each with arugula salad and generous drizzle of the balsamic reduction.